Question: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x - 7)^2 - 4$
Explanation: The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x - 7)^2 - 4 = 0$ Add $4$ to both sides so we can start isolating $x$ on the left: $ (x - 7)^2 = 4$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x - 7)^2} = \pm \sqrt{4}$ Be sure to consider both positive and negative $2$ , since squaring either one results in $4$ $ x - 7 = \pm 2$ Add $7$ to both sides to isolate $x$ on the left: $ x = 7 \pm 2$ Add and subtract $2$ to find the two possible solutions: $ x = 9 \text{or} x = 5$